论文标题
变形理论中的Maurer-Cartan方法：扭曲过程
Maurer-Cartan methods in deformation theory: the twisting procedure
论文作者
论文摘要
该专着提供了有关代数，几何，拓扑和数学物理学中毛勒 - 卡丹方法的概述。它为扭曲过程提供了一种概念，详尽和温和的处理，该方法可从毛rer族 - 玛格 - - 卡丹元素创建新的差分级级代数，联想代数或同型版本（以及它们的同型版本）。通过有史以来最大的变形量规组的作用来描述（同型）联想代数或（同型）lie代数的扭曲程序。我们给出了有关其相关代数类别的有意义的扭曲程序的二次作业的标准。而且，我们使用新的更简单的演示文稿介绍了Willwacher的扭曲过程，该过程为我们提供了与图形同源性相关的广泛激励示例，既恢复已知的图形复合物（由于Kontsevich）并引入了一些新的。本书始于使用差分分级谎言代数的量规理论和变形理论的基本调查，以简化通往理论的方式。它以对变形理论的基本定理，更高的谎言理论，合理同义理论，同型代数的简单理论和拉格朗日亚曼氏群的浮动共同体结束。
This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry, topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment of the twisting procedure, which functorially creates new differential graded Lie algebras, associative algebras or operads (as well as their homotopy versions) from a Maurer-Cartan element. The twisting procedure for (homotopy) associative algebras or (homotopy) Lie algebras is described by means of the action of the biggest deformation gauge group ever considered. We give a criterion on quadratic operads for the existence of a meaningful twisting procedure of their associated categories of algebras. And, we introduce the twisting procedure for operads à la Willwacher using a new and simpler presentation, which provides us with a wide source of motivating examples related to graph homology, both recovering known graph complexes (due to Kontsevich) and introducing some new ones. This book starts with elementary surveys on gauge theory and deformation theory using differential graded Lie algebras in order to ease the way to the theory. It finishes with concise surveys on the fundamental theorem of deformation theory, higher Lie theory, rational homotopy theory, simplicial theory of homotopy algebras, and the Floer cohomology of Lagrangian submanifolds, to illustrate deep examples of applications.
